A. Find the Laplace transforms of the given functions. 1. f(t) = 6e^(-5t)+e^3t+5(t^3)-9 2. g(t) = 4cos(4t)–9sin(4t)+2cos(10t) 3. h(t) = e^3t+cos(6t)–e^(3t)cos(6t)

Q: Find the Laplace transform of cos 5t

A: To find the Laplace transform of cos 5t.

Q: e-2t cos 3t cOS

A: The given question is related to Laplace Transform. The solution is explained below.

Q: Find the Laplace transform of: 1. f(t) = e(-3t) sin(2t) cos(3t) cosh(t)

A: Given that 1) f(t) = e-3tsin (2t) cos (3t) cosh (t) 2) f(t) = 1+sin t + (8t)15 + t2cos 3t We have to…

Q: Find the Laplace transform of L(t5)

A: The Laplace Transform of f(t) is given by, L{f(t)}=   ∫∞ 0   e^-stf(t)dt Here f(t)=t^5 So, L(t^5)= ∫…

Q: B: Find Laplace Transform of f(t)= cos3t By DEF.

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Q: Find the Laplace Transform of: e-2 -2t sin2t + e3tt2

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Q: Find the Laplace transform of the following: 1. e3t cos 2t 2. sinh3 4t 3. te-lu(t – 1) 4. t cosh 2t

A: 1) Given:    e3tcos 2t      Applying Laplace transform       Lft=Le3tcos 2t Apply transform rule:…

Q: Find the Laplace transform of: 1. f(t) = e(-4t)[sin(2t) – cos(2t)]?

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Q: 5) Evaluate te " cos 3tdt using Laplace Transform! -4t

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Q: 1 Find the Inverse Laplace Transform of s2+2s+ 10 -'cos3t B -Isin9t 3 cost 9 -'sin3t (D 3

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Q: 2) There is a function F (s) with "different true root state". Make the inverse laplace transform of…

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Q: Question included in image

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Q: 7. Given that the Laplace transform of te is F(s) =- (s + k) Laplace transform of te" without using…

A: The solution is given as

Q: 1 5. If the Laplace transform of f(t) = , find F(4s) %3D

A: We have given that , Laplace transform of , f(t)  is e1ss. We need to find  ,  F(4s). We know that ,…

Q: Find the Laplace transform of 4 sin(3t)+2 cos(9t).

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: 7s2 – 3s + 26 F(s) (8 – 1)(s² + 9)

A: Explanation of the solution is given below...

Q: Solve the Laplace transform of: 4 sinh 3t + 3 cosh 3t

A: Introduction: The Laplace transformation of sinh(at) and cosh(at) is given by,…

Q: Determine the Laplace Transform of est cos 5t .

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Q: Solve for the Laplace transform of e2t sint cost cos 2t cos 4t 1 s-4s+20 s-4s+68 -4s+20

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Q: Use the Laplace transform to solve the given initial-value problem. Use the table of Laplace…

A: Given differential equation is  y''+25=cos(5t) with initial conditions y(0)=3 , y'(0)=2 we have to…

Q: 8 3 Find the Inverse Laplace Transform of- + 3s2+ 12 s2– 49 3 4 A) - sin2t + -cosh ( 7t) 7 3 4 –…

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Q: Consider the IVP: y" - y' + 2y = 8sin(2t) - 8, with y(0) = -2, y'(0) = -4. Solve the IVP by using…

A: Given IVP is y''-y'+2y=8sin2t-8              (i) With y0=-2, y'0=-4 Taking Laplace transformation of…

Q: 1. Show that the function 2t et cos (et“) is not of exponential order, however its Laplace transform

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Q: Solve for the Laplace transform of et sint cost cos 2t cos 4t 7+4s+20 82-4+20 -4+68 4s+8

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Q: Solve X'= %3D 1 2. 人 2. Given use %3D -2-2 Laplace TransForm OF A to Compute At.

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Q: Find the Laplace transform of (cosht + 1)2.

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Q: Find the Fourier transform for S(2)%3D sin a, 2 0.

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Q: What is the value of the inverse Laplace transform given by L 2s+1 8 J s2 +2s +3 O a. e-t (2…

A: Some Laplace inverse transform formulas: L-1(s-a)(s-a)2+b2=eatcosbtL-1b(s-a)2+b2=eatsinbt

Q: Determine the Laplace transform of L(sinh 5t * cos t)

A: Explanation of the answer is as follows

Q: i) Find the Fourier sine transform of (sinx, 0a %3D au Courier Transforms, Calculate

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Q: 22) Solve the initiai value problem by Laplace transform. y"+4y cos 2t y(0) =1, y'(0) = 1

A: In this question, we are asked to solve the Initial value problem by Laplace transform Equation :…

Q: y Ct) = 5€ - 2t Cos 6t

A: Use the following 1.L{cos at}=ss2+a22.If L{f(t)}=F(s)Then L{eatf(t)}=F(s-a)

Q: 3.1 If the Laplace transform of coswt is then find the Laplace Transform of the s2+w? following…

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Q: 25. а. Apply Fourier transform to solve: ди for 0 < x, t 20 Under the conditions,

A: Given,              ∂u∂t=∂2u∂x2,  for  0≤x, t≥0           (1)Under the conditions,…

Q: VE cos(3f). find the Laplace transform of %3D

A: Laplace transformation is a method used for obtaining the solution of a complex differential…

Q: 3. Find the inverse Laplace transform of: 2s2 + 3s - 5 F(s) = s(s + 1)(s – 2)

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Q: Show that (a) L-1 = sin(at) - tcos(at) %3D (s²+a²)²) (where L indicates imverse Laplace transform)…

A: L-11s2+a22=12a2sin(at)-12a2tcos(at)

Q: Give the Laplace transform of -2x 0Sx and x < 3 f(x) = 4 3<x -3s 27 20 O F(s) = -- b) O F(s) = - -3s…

A: Solution :-

Q: Which is the correct inverse Laplace transform of U (s)=+ O u(t) = 6t + sinh(4t) + cosh(4t) %3D O u…

A: Recall:  L-11sn=tn-1(n-1)! L-1ss2+a2=cos at L-11s2+a2=1asin at

Q: 2. Find L{e3t cos 2t} using property of Laplace transform

A: We’ll answer the first question (Question number 2) since the exact one wasn’t specified. Please…

Q: Solve for the Laplace transform of e2t sin t cost cos 2t cos 4t

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Q: What is the Laplace transform of 7sin (6 t) sinh(6 t)

A: What is the Laplace transform of 7sin (6 t) sinh(6 t)

Q: find the Laplace transform of (sinx - cosx)² O (s² - 2s + 4)/s(s+ 4) (s² + 2s + 4)/s (s² - 4) O (s²…

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Q: Q3: Find the solution of the Laplace transforms of the following functions: L-1 ¹ [-35 -3s2-12s-87…

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Q: 3) There is a function F (s), which is a 'folded or repeated root state". Make the inverse laplace…

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Q: 4. Find the Laplace transforms of a) Sinh 3t cos²t | cos (t-2n/3), b) t > 2t/3 14, c) t'e'sin6t. t <…

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Q: Prove that the Laplace Transform of ´cos(bt) is S-a (s-a)° +b² Please show your solution clearly.

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Q: 9. Find the mverse laplace transform of system function HS) = for 3 cases of ROCs when- s45s+6 (1)…

A: Consider the given function. Hs=1s2+5s+6 Find the factor of the denominator.…

Q: Solve for the inverse Laplace transform of O 4cos at - 3 sin at 4 sin at – 3 cos at 3cos at - 4 sin…

A: It is known that: L-1a·fs+b·gs=a·L-1fs+b·L-1gsL-1ss2+a2=cosatL-1as2+a2=sin(at)

Q: 4. Use Laplace transform technique to solve , y"+2y'+2y = e given y(0) = -2 and y'(0) =-1 %3D

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